Every lens space contains a genus one homologically fibered knot
Geometric Topology
2019-04-22 v2 Number Theory
Abstract
We prove that every lens space contains a genus one homologically fibered knot, which is contrast to the fact that some lens spaces contain no genus one fibered knot. In the proof, the Chebotarev density theorem and binary quadratic forms in number theory play a key role. We also discuss the Alexander polynomial of homologically fibered knots.
Keywords
Cite
@article{arxiv.1702.02731,
title = {Every lens space contains a genus one homologically fibered knot},
author = {Yuta Nozaki},
journal= {arXiv preprint arXiv:1702.02731},
year = {2019}
}
Comments
13 pages, 3 figures